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Select the correct answerA villager buys a goat and a sheep together for Rs.14,250. He sold the sheep at a profit of 10% and the goat at a loss of 20%. If he sold both the animals at the same price, then what was the cost price of the cheaper animal?Options8,2507,5006,0006,600

Question

Select the correct answerA villager buys a goat and a sheep together for Rs.14,250. He sold the sheep at a profit of 10% and the goat at a loss of 20%. If he sold both the animals at the same price, then what was the cost price of the cheaper animal?Options8,2507,5006,0006,600

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Solution

Let's denote the cost price of the sheep as S and the cost price of the goat as G.

According to the problem, S + G = 14,250.

The sheep was sold at a profit of 10%, so its selling price was 1.1S. The goat was sold at a loss of 20%, so its selling price was 0.8G.

Since both animals were sold for the same price, we can set these two equations equal to each other:

1.1S = 0.8G

Now we have a system of two equations, and we can solve it step by step.

First, let's express S from the first equation: S = 14,250 - G.

Now we can substitute S in the second equation:

1.1(14,250 - G) = 0.8G

This simplifies to:

15,675 - 1.1G = 0.8G

Combine like terms:

15,675 = 1.9G

Finally, solve for G:

G = 15,675 / 1.9 ≈ 8,250

So, the cost price of the goat was approximately Rs.8,250.

Substitute G = 8,250 in the first equation to find S:

S = 14,250 - 8,250 = 6,000

So, the cost price of the sheep was Rs.6,000.

Therefore, the cost price of the cheaper animal was Rs.6,000.

So, the correct answer is 6,000.

This problem has been solved

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